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DOI: 10.4230/LIPIcs.ICDT.2025.20

A Formal Language Perspective on Factorized Representations

Authors: Benny Kimelfeld, Wim Martens, and Matthias Niewerth

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract

Factorized representations (FRs) are a well-known tool to succinctly represent results of join queries and have been originally defined using the named database perspective. We define FRs in the unnamed database perspective and use them to establish several new connections. First, unnamed FRs can be exponentially more succinct than named FRs, but this difference can be alleviated by imposing a disjointness condition on columns. Conversely, named FRs can also be exponentially more succinct than unnamed FRs. Second, unnamed FRs are the same as (i.e., isomorphic to) context-free grammars for languages in which each word has the same length. This tight connection allows us to transfer a wide range of results on context-free grammars to database factorization; of which we offer a selection in the paper. Third, when we generalize unnamed FRs to arbitrary sets of tuples, they become a generalization of path multiset representations, a formalism that was recently introduced to succinctly represent sets of paths in the context of graph database query evaluation.

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Benny Kimelfeld, Wim Martens, and Matthias Niewerth. A Formal Language Perspective on Factorized Representations. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kimelfeld_et_al:LIPIcs.ICDT.2025.20,
  author =	{Kimelfeld, Benny and Martens, Wim and Niewerth, Matthias},
  title =	{{A Formal Language Perspective on Factorized Representations}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.20},
  URN =		{urn:nbn:de:0030-drops-229614},
  doi =		{10.4230/LIPIcs.ICDT.2025.20},
  annote =	{Keywords: Databases, relational databases, graph databases, factorized databases, regular path queries, compact representations}
}

Document

DOI: 10.4230/LIPIcs.STACS.2020.7

A Trichotomy for Regular Trail Queries

Authors: Wim Martens, Matthias Niewerth, and Tina Trautner

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract

Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class T_tract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan et al. [Bagan et al., 2013]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice.

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Wim Martens, Matthias Niewerth, and Tina Trautner. A Trichotomy for Regular Trail Queries. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{martens_et_al:LIPIcs.STACS.2020.7,
  author =	{Martens, Wim and Niewerth, Matthias and Trautner, Tina},
  title =	{{A Trichotomy for Regular Trail Queries}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.7},
  URN =		{urn:nbn:de:0030-drops-118681},
  doi =		{10.4230/LIPIcs.STACS.2020.7},
  annote =	{Keywords: Regular languages, query languages, path queries, graph databases, databases, complexity, trails, simple paths}
}

Document

DOI: 10.4230/LIPIcs.ICDT.2019.22

Constant-Delay Enumeration for Nondeterministic Document Spanners

Authors: Antoine Amarilli, Pierre Bourhis, Stefan Mengel, and Matthias Niewerth

Published in: LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)

Abstract

We consider the information extraction framework known as document spanners, and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential variable-set automaton (VA). We pose this problem in the setting of enumeration algorithms, where we can first run a preprocessing phase and must then produce the results with a small delay between any two consecutive results. Our goal is to have an algorithm which is tractable in combined complexity, i.e., in the sizes of the input document and the VA; while ensuring the best possible data complexity bounds in the input document size, i.e., constant delay in the document size. Several recent works at PODS'18 proposed such algorithms but with linear delay in the document size or with an exponential dependency in size of the (generally nondeterministic) input VA. In particular, Florenzano et al. suggest that our desired runtime guarantees cannot be met for general sequential VAs. We refute this and show that, given a nondeterministic sequential VA and an input document, we can enumerate the mappings of the VA on the document with the following bounds: the preprocessing is linear in the document size and polynomial in the size of the VA, and the delay is independent of the document and polynomial in the size of the VA. The resulting algorithm thus achieves tractability in combined complexity and the best possible data complexity bounds. Moreover, it is rather easy to describe, in particular for the restricted case of so-called extended VAs.

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Antoine Amarilli, Pierre Bourhis, Stefan Mengel, and Matthias Niewerth. Constant-Delay Enumeration for Nondeterministic Document Spanners. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{amarilli_et_al:LIPIcs.ICDT.2019.22,
  author =	{Amarilli, Antoine and Bourhis, Pierre and Mengel, Stefan and Niewerth, Matthias},
  title =	{{Constant-Delay Enumeration for Nondeterministic Document Spanners}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-101-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{127},
  editor =	{Barcelo, Pablo and Calautti, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.22},
  URN =		{urn:nbn:de:0030-drops-103246},
  doi =		{10.4230/LIPIcs.ICDT.2019.22},
  annote =	{Keywords: enumeration, spanners, automata}
}

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Documents authored by Niewerth, Matthias

A Formal Language Perspective on Factorized Representations

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A Trichotomy for Regular Trail Queries

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Constant-Delay Enumeration for Nondeterministic Document Spanners

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